Let's face it, cooking is not the hard part, it's doing the dishes that makes most people not want to cook!
The solution for this is to devise simple techniques, and plan out when things get clean. Most food needs time to cool, and most people are too stuffed to move after they are done eating. For this reason. Here is the best stragies I know.
Transfering the meal into serving dishes right away, can free up the pans to be soaked, or cleaned while the food cools. Leaving food in the pot or pan it was cooked in can significantly contribute to cleaning time later on.
Most high-quality cooking involves pauses or down-time while letting the heat modify the ingredients. The cutting board and side-dishes that have finished already, are usually candidates for cleaning at times when there are free-hands to do so.
Avoiding the dish-washer can mean that you clean items as they are needed and avoid a pile-up. The age old "is the dish-washer clean" can cause most of your dishes, cutlerty, or pans to be in no-ones-land wondering if they are usable or not.
Rinse, Soap, Rinse is the three step method, where you get the food off a dish with water running, turn off the water and wash the dishes with a soapy sponge, and then rins the mostly-clean soapy dishes. This can also be done with a soak-step in hot water for an extra sanitary clean. The process is quick and easy to manage, especially with a two-compartment sink.